The discussion focuses on applying the Stolz-Cesaro theorem to find the limit of the sequence defined as (xn) = (cos(π/n+1) + cos(π/n+2) + ... + cos(π/2n))/n as n approaches infinity. Participants clarify that the limit involves evaluating cos(π/2n+1) + cos(π/2n+2) - cos(π/n+1). Additionally, it is emphasized that the Stolz-Cesaro theorem must be applied in conjunction with another sequence for proper evaluation.
PREREQUISITESStudents studying calculus, particularly those focusing on sequences and limits, as well as educators looking to enhance their understanding of the Stolz-Cesaro theorem and its applications.
What you wrote in the first term was ##\cos(\frac{\pi}{n} + 1)##, and similar in the other two terms. Is that what you intended?LazuRazvan said:Homework Statement
hello, i have to find the limit of the next array
(xn)=(cos (π/n+1) + cos (π/n+2) + ...+ cos ( π/2n))/n
Same comment as above.LazuRazvan said:when n goes to infinity.
Homework Equations
I was told to apply stolz cesaro and that is where i ended up :
the limit is :
limit of cos ( π/2n+1) + cos (π/2n+2) -cos (π/n+1)
LazuRazvan said:The Attempt at a Solution
How i finish this ?